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Full text of "Analytical Mechanics"

72                         ANALYTICAL MKCHANK'ri
PROBLEMS.
1.   A weight of 5 tons is to be raised from the hold of a ship by means of a rope which takes 3| turns around the drum of a steam windlass.    If At = 0.25 what force must a man exert at the other end of the rope?
2.   By pulling with a force of 200 pounds a man just, keeps from surging a rope, which takes 2.5 turns around a post.    Find the tensile force* at the other end of the rope,   ju = 0-2.
3.  A weight W is suspended by a rope which makes 1J turns around a clamped pulley and goes to the hand of a workman.    If ju     0.2, find the force the man has to apply in order (a) to support the weight, (b) to raise it.
4.   Two men, each of whom can exert a pull of 1250 pounds, can support a weight by means of a rope which takes 2 turns around a post. •On the other hand, one of the men can support it alone if the rope makes 2.5 turns.   Find the weight.
5.  In order to prevent surging a sailor has to exert a force of 150 pounds at the end of a hawser, which is used to keep (he .stern of a boat .at rest while the bow is being turned by the engines.    Find flu* pull •exerted by the boat upon the hawser under the following conditions;
[Hint. — Make use of equations (5) <nul ('!»),] (a)«-f.
(b)   fl = |,
(c)   0 = |,
(d)  0=T,
(e)  B-6-},
(f)  0 = Y'
6.  A belt has to transmit an effective; fora- of ,r>(H) pounds,    Find tin-tensile force on both sides of the bolt, under the following condition.*:
(a)  8 = 135°,     n = 0.5.           (c) 0 -,- iiif)0,     M   - {).:>.
(b)  6 = 135°,     n = 0.4.           (f)  0 ^ i,s(l",     M   , (),;{.
(c) 0 = 150°,   /i-0.3.       (K) e - ING",   At   ».-,.
(d) 6 = 165°,     n = 0.5.          (h) 0 - l!ir»°,     p     ()..j.
7.   In the preceding problem find the width of the- hcli, .s.ippomng the permissible safe tensile force to be 50 pounds per inch of its width.
= 0.2.	(g)  fl-ojr,
= 0.5.	(h)  fl-Y'
= 0.5,	0) e :,-. *f,
= 0.4.	(j) 0-:**,
= 0.3.	(k) 0 =, I:J=
= f) 9.	m  ft     ^w^